From 6c855f985c7c4d5217ff85382d4f62cdf808507a Mon Sep 17 00:00:00 2001
From: "Claudius \"keldu\" Holeksa" <mail@keldu.de>
Date: Wed, 18 Jun 2025 16:34:48 +0200
Subject: Initial commit copied from my godbolt impl

---
 c++/lights_out.cpp | 171 +++++++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 171 insertions(+)
 create mode 100644 c++/lights_out.cpp

diff --git a/c++/lights_out.cpp b/c++/lights_out.cpp
new file mode 100644
index 0000000..9b8503f
--- /dev/null
+++ b/c++/lights_out.cpp
@@ -0,0 +1,171 @@
+#include <vector>
+#include <array>
+#include <numeric>
+#include <iostream>
+
+constexpr size_t M = 3;
+constexpr size_t N = 3;
+constexpr size_t MN = M * N;
+using Mat = std::array<std::array<bool,MN>,MN>;
+using Vec = std::array<bool,MN>;
+
+struct point {
+    point():x{0},y{0}{}
+    point(size_t x_, size_t y_):x{x_},y{y_}{}
+
+    size_t x,y;
+
+    point& inc() {
+        point& ret = *this;
+
+        ++y;
+        if(y >= N){
+            ++x;
+            y -= N;
+        }
+
+        return *this;
+    }
+
+    size_t stride() const {
+        return x + y*N;
+    }
+
+    bool equal(const point& rhs) const {
+        return (x == rhs.x && y == rhs.y);
+    }
+};
+
+void print_vec(const Vec& x){
+    for(size_t j = 0; j < N; ++j){
+        for(size_t i = 0; i < M; ++i){
+            point ind{i,j};
+            std::cout<<x[ind.stride()]<<" ";
+        }
+        std::cout<<"\n";
+    }
+    std::cout<<std::endl;
+}
+
+void print_perm(const std::array<size_t,MN>& x){
+    for(size_t j = 0; j < MN; ++j){
+        std::cout<<x[j]<<"\n";
+    }
+    std::cout<<std::endl;
+}
+
+void print_mat(const Mat& x, const std::array<size_t,MN>& P){
+    for(size_t j = 0; j < MN; ++j){
+        for(size_t i = 0; i < MN; ++i){
+            std::cout<<x[P[j]][i]<<" ";
+        }
+        std::cout<<"\n";
+    }
+    std::cout<<std::endl; 
+}
+
+bool lu_decompose_gf2(Mat& R, std::array<size_t,MN>& P){
+    for(size_t i = 0; i < MN; ++i){
+        bool found_pivot = false;
+        size_t pivot_row = i;
+        for(size_t k = i; k < MN && (not found_pivot); ++k){
+            if(R[P[k]][i]){
+                found_pivot = true;
+                pivot_row = k;
+            }
+        }
+        if(not found_pivot){
+            return false;
+        }else if ( i != pivot_row ){
+            std::swap(P[i],P[pivot_row]);
+        }
+        for(size_t k = i+1u; k < MN; ++k){
+
+            if(R[P[k]][i]){
+                for(size_t j = i+1u; j < MN; ++j){
+                    R[P[k]][j] ^= (R[P[i]][j]);
+                }
+            }
+        }
+    }
+
+    return true;
+}
+
+int main(){
+    Mat A;
+    
+    Vec b{
+        1,0,1,
+        1,0,1,
+        0,0,0
+    };
+
+    // Works best if we use odd N's
+    // even N might not be solvable in roughly half of the cases
+    // Init
+    std::cout<<"Init"<<std::endl;
+    for(point i{}; i.x < M && i.y < N; i.inc()){
+        for(point j{}; j.x < M && j.y < N; j.inc()){
+            if(
+                (i.equal(j)) ||
+                (i.x == j.x && (i.y+1) == j.y) ||
+                (i.x == j.x && (j.y+1) == i.y) ||
+                (i.y == j.y && (i.x+1) == j.x) ||
+                (i.y == j.y && (j.x+1) == i.x)
+            ){
+                A[i.stride()][j.stride()] = true;
+            }else{
+                A[i.stride()][j.stride()] = false;
+            }
+            // std::cout<<A[i.stride()][j.stride()]<<std::endl;
+        }
+        // Populate how you like it.
+        //b[i.stride()] = false;
+    }
+    std::array<size_t, MN> P_ident;
+    std::iota(P_ident.begin(),P_ident.end(),0);
+    print_mat(A,P_ident);
+
+    std::array<size_t, MN> P;
+    std::iota(P.begin(),P.end(),0);
+    // Solve it :)
+    std::cout<<"Solve"<<std::endl;
+    if(!lu_decompose_gf2(A,P)){
+        return -1;
+    }
+    std::array<size_t,MN> P_inv{};
+    for(size_t i = 0; i < MN; ++i){
+        P_inv[P[i]] = i;
+    }
+
+    std::cout<<"LR"<<std::endl;
+    print_mat(A,P);
+
+    std::cout<<"P"<<std::endl;
+    print_perm(P);
+
+    std::cout<<"Lights-Off puzzle"<<std::endl;
+    print_vec(b);
+
+    Vec y;
+    for(size_t i = 0; i < MN; ++i){
+        y[i] = b[P[i]];
+        for(size_t j = 0; j < i; ++j){
+            y[i] ^= A[P[i]][j] & y[j];
+        }
+    }
+
+    Vec x;
+    for(size_t i = MN; i > 0; --i){
+        x[i-1] = y[i-1];
+        for(size_t j = i; j < MN; ++j){
+            x[i-1] ^= (A[P[i-1]][j] and x[j]);
+        }
+    }
+
+    std::cout<<"Solution"<<std::endl;
+    print_vec(x);
+
+    return 0;
+}
-- 
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